The Gaseous Stateof Matter

Preparation for College ChemistryColumbia UniversityDepartment of Chemistry

Chapter Outline

KMT

Gas Laws

Ideal Gas Equation

Gas Stoichiometry

Air Pollution

Preliminary Observations

Molar mass of water: 18g /mole

6.02x1023 molecules weigh 18g

Density of water: 1g/cc

18 g liquid water occupies 18mL

18 g gaseous water occupies 22,400mL

Kinetic Molecular Theory of Gases

KE =1

2m c =

2p = m c

p

2m

2

v=+10cm/s

c=10cm/s

Wall

-x +x

{v=-10cm/sc=10cm/s

12

mc2 = 32

kT

Kinetic Molecular Theory of Gases

0 600 1000 1400 1800200

0.4

0.6

0.8

1.0

1.2

1.4

Molecular Speed

# M

olec

ule

s

O2 at 1000°C

O2 at 25°C

Distribution of Molecular Speeds

RategasARategasB

=dBdA

=MB

MA

Graham’s Law of Effusion

At the same T and P, the rates of Effusion of two gases are inversely proportional to their densities or molar masses.

VacuumGas

Naturally occurring Uranium : U-235 / U238 = 1 / 140

2nd step: Effusion through thousands of membranes (cascades)

1st step: U + 6 F 235 UF6 238 UF6 (g)

R235−UF6

R238−UF6

=m238−UF6

m235−UF6

=352349

=1.0043

3rd step: 235 UF6

235U Fully enriched weapons-grade Uranium

State Variables

V = volume (liters, cm3, m3)

T = temperature (in K)

P = pressure (atmospheres, mmHg, kPa)

101.325 mbar

29.9 in. Hg

14.7 lb/in2 (PSI)

76 cmHg

760 mmHg760 torr

1 atm

Torricelli’s barometer

At sea level

Atmospheric Pressure

150 kmHg height

air

0 1 3 5 7

Pressure (atm)

9

1

2

3

4

5

6

Vol

um

e (L

)

0

7

Boyle’s Law

P x V = k

At Constant TFor an Ideal Gas

P1 x V1 = P2 x V2

P1

V2

P2

V1

=

1

2

3

4

5

6

Vol

um

e (L

)

0

7

-300

T (°C)

-100 100 300 500

Charles’ Law At Constant P for an Ideal Gas

V = kT

V1

T1

V2

T2

=V T

-273°C

Absolute zero

0

1

2

3

4

5

6

Pre

ssu

re (

atm

)

7

-300

T (°C)

-100 100 300 500

P = kT

P1

T1

P2

T2

=

Gay-Lussac’s Law

At Constant V for an Ideal Gas P T

Combined Gas Laws

V1

T1

V2

T2

=

P2 V2

T2

=P1 V1

T1

Charles’ Boyle’s

V1 P1 T2

P2 T1

=V2

P1 V1 = P2 V2

STP Conditions

Standard Temperature: 273.15 K= 0.00°C

Standard Pressure: 1 atm

Reference Points for T and P for comparison

Dalton’s Law of Partial Pressures

Ptot = P1 + P2 + P3 + ...

where P1 is the partial pressure of gas 1, etc...

Pgas = Ptotal – PH2O

where PH2O is the vapor pressure of water at the specified

temperature. Most often used in collection of insoluble gases

over water. In open systems, Ptotal = Patm

Pn = Xn Ptotal

Xn =nn

n1 + n2 + n3 + ...

Molar fraction of gasn

Gay-Lussac’s Law of combining volumes

Avogadro’s Law

1809

1811

“When measured at the same T and P, the ratios of the V of reacting gases are small whole numbers”

“Equal volumes of different gases at the same T and P containthe same number of molecules”

Vn

=constant

Consequences of Avogadro’s Law

1. Explanation of Gay-Lussac’s combining volumes law. Diatomic nature of elemental gases.

2. Method for determining molar masses of gases. The molar Volume.

3. Firm foundation of KMT: gases consists of microscopic particles

Density of Gases

dV

=m

But V = f (P, T) dgasT ,P

Gas M(g/mol) d(g/L)

STPGas M(g/mol)

STPd(g/L)

H2

CH4

NH3

C2 H2

HCNCO

N2

air

H2S

HCl

F2

CO2

C3 H8

O3

SO2

Cl2

2.016)16.0417.03

26.04

27.03

28.01

28.02

28.9

32.00 1.4370.90 3.17

2.86

2.14

1.97

1.96

1.70

1.63

1.5234.09

36.46

38.00

44.01

44.09

48.00

64.071.25

1.25

1.21

1.16

0.760

0.716

0.900

1.29O2

1

PV

Ideal Gas Equation

TV

For one mole of a gas at STP, R constant:

(1 atm)(22.4L)

273K=R = 0.082

L-atm

mol-K

nV nT

P=V R

nT

PV

=R TP V m

M

= n R TP V

=R T

MmPV

=PM

dRT

Equation of State

Ideal Gas Equation

[pressure][Volume]

[temperature][mol]=[R] =

[force][volume]

[area][temperature][mol]

=[force][length]

[temperature][mol]=

[energy]

[temperature][mol]

R = 8.134 J mol-1 K-1 ~ 2 Cal mol -1 K-1

The ideal gas constant has energy/mol degrees dimensions

[R]

Gas Stoichiometry

Cu(s) + 4H+ + 2NO3- (aq) Cu+2 (aq) + 2NO2 (aq) + 2H2O

Concentrated nitric acid acts on copper and produces nitrogen dioxide and dissolved copper. 6.80 g Cu is consumed and NO2 is collected at a pressure of .970atm and a temperature of 45°C (318 K) . Calculate the volume of NO2 produced.

63.55 g Cu

1 mol Cux6.80 g Cu x

1 mol Cu

2 mol NO2 = 0.214 mol NO2

n R T

P=V = 5.76 L NO2

http://www.sp.uconn.edu/~terry/229sp98/Ncycleanim.html

Real Gases

Follow the ideal gas law at sufficiently low densities

Gas molecules attract one another

Both factors increase in importance when the molecules are close together (high P. low T).

Gas molecules occupy a finite volume

n R T

P V=z

Deviations from ideality are quantified by the Compressibility factor z

Real Gases Intermolecular Forces

0

0.5

1.0

1.5

Com

pres

ibil

ity

rati

o

2.0

0

P (atm)200 400 600 800

Ideal Gas

H2

CH4

N2

0

0.5

1.0

1.5

Com

pres

ibil

ity

rati

o2.0

0

P (atm)200 400 600 800

Ideal Gas

600 °C

-100 °C

25 °C

Nitrogen at several T

Van der Waals Equation

P +an2

V2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ V −nb( ) =nRT

b = constant representing volume excluded per mole of molecules

a = depends on the strength of attractive forces

n2

V2Proportional to reduction of wall collisions due to cluster formation.

Air Pollution

O2

2O

O2 O+ O3

O2O+O3

+ heat

CCl3F

CCl2F + Cl .

Cl . + O3 ClO . + O2

ClO . + O O2 + Cl .

Allotropic Transformation

Ozone shield

Ozone destruction